No, we are all really as stupid as you Europeans think that we are. If the invitation does not blow up by a certain date, we don't know what to do with it. . I would assume that most Americans know what RSVP means.

I think (hope) most Americans know what RSVP means. However, no matter how you phrase it ("RSVP," "the courtesy of a response is requested by [date]", "you need to tell me if you're coming", etc.), you will always get a minority of people who never respond. What's just as bad, if not worse, is people who say they will show up, but then don't without a good excuse, particularly if the event is costing a set amount per plate.

Wait a minute, I thought the whole point of "RSVP" was that you only have to respond if you want to. If it literally means "respond, if it pleases you" or "respond, if you please," what if it doesn't please me to respond or if I don't please to respond?

If you really want everyone to respond, don't ask in such a weak, french, way (i.e., "respond, if you please"), ask in a tough American way (e.g., "a response is mandatory" or "failure to respond will result in legal action" or "failure to respond may result in death or serious injury").